Intelligent Virtual Machine (VM) provisioning is central to cost and resource efficient computation in cloud computing environments. As bootstrapping VMs is time-consuming, a key challenge for latency-critical tasks is to predict future workload demands to provision VMs proactively. However, existing AI-based solutions tend to not holistically consider all crucial aspects such as provisioning overheads, heterogeneous VM costs and Quality of Service (QoS) of the cloud system. To address this, we propose a novel method, called CILP, that formulates the VM provisioning problem as two sub-problems of prediction and optimization, where the provisioning plan is optimized based on predicted workload demands. CILP leverages a neural network as a surrogate model to predict future workload demands with a co-simulated digital-twin of the infrastructure to compute QoS scores. We extend the neural network to also act as an imitation learner that dynamically decides the optimal VM provisioning plan. A transformer based neural model reduces training and inference overheads while our novel two-phase decision making loop facilitates in making informed provisioning decisions. Crucially, we address limitations of prior work by including resource utilization, deployment costs and provisioning overheads to inform the provisioning decisions in our imitation learning framework. Experiments with three public benchmarks demonstrate that CILP gives up to 22% higher resource utilization, 14% higher QoS scores and 44% lower execution costs compared to the current online and offline optimization based state-of-the-art methods.